It is technically 'possible' - taking into consideration elements diameter and overall massiveness of the lens..The reason you do not see it is because it is not 'necessary'.

The sensor/film is being provided more light by a wide angle lens to begin with, so it is not necessary from an exposure stand point.

Wide angle lenses have a greatly distorted depth of field by the laws of physics, this would not be changed by a wide aperture. You would simply end up with little more than a small 'area' of the image in focus with the remainder falling out of focus so rapidly that every image would look like impaired vision - it is one of the primary reasons t/s lenses were invented.

From a creative stand point, you can achieve the same thin dof 'effect' with a wide angle lens by simply getting as close as you can to your subject. The effect would be the same on the background elements of the image whether at f/1.8 or f/2.8, the difference being essentially imperceptible.

I think the misconception in desiring such a lens is the expectation that one would get the same flatness of the focal plane at 14mm as seen in 35mm or 50mm - there is a big difference in the curvature of perspective between 35mm and 14mm. The focal plane would wrap around the sides to the extent that nothing would appear in focus except the single point that you were actually looking at - similar to your own eye.

TO back this up, the only f/1.8 lens I am aware of at wider than 24mm is the 20mm f/1.8 that Sigma has, and the reviews lean towards the "suck" side of things. And that's not a zoom and not going to 14mm. Seeing how insanely large the element is at 14mm f/2.8 on the Nikon zoom, I'd shutter to think what it'd be at f/1.8

Shallow DOF helps isolate the subject, no matter the focal length. I notice a big difference between f1.8 and f2.8 @ 50mm. I imagine such a difference would exist also at 15mm.

Except at 50mm, your focus plane is maybe a foot wide at f/1.8, so, you can isolate an object fairly easily. At 15mm, your plane is now 10ft in length, so trying to isolate that same object would fail. The background would have to be 10x as far away to get a similar effect.

I'm guessing you haven't shot ultra-wide; the reality is that even at f/2.8 on anything wide than 20mm, you can pretty much set focus about 1/3 to 1/2 way into a scene and get everything in focus. Not much isolation to be had in the ultra-wide realm without T/S

C. I don't see the benefit of shallow DOF for ultrawide. Could you enlighten me?

Shallow DOF helps isolate the subject, no matter the focal length. I notice a big difference between f1.8 and f2.8 @ 50mm. I imagine such a difference would exist also at 15mm.

Yes, but only in very close focus distances.

On 14mm f/1.8 you would have to focus closer than 3.68 meters because on and after that focus distance the focus extends to infinity. In other way, on that focus distance, anything from 1.84 meters to infinity would be in focus.

The closest focus distance for 14mm f/2.8 that focuses to infinity is 2.33 meters and anything from 1.16 meters to infinity would be in focus.

If you focus really close, say at one meter with 14mm, the depth of field for f/1.8 is about half (0.58 meters) of the f/2.8 depth of field (1.04 meters) so you would get a shallower DOF, but you would be limited to shoot subjects closer than 1.16 meters to get the shallow DOF.